2021/08/26 by Jenia Tevelev, Tevelev, Jenia, Sebastián M. Torres +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2108.11951
Let C be a smooth projective curve of genus g≥2 and let N be the moduli space of stable rank 2 vector bundles on C of odd degree. We construct a semi-orthogonal decomposition of the bounded derived category of N conjectured by Narasimhan and by Belmans, Galkin and Mukhopadhyay. It has two blocks for each i-th symmetric power of C for i=0,…,g-2 and one block for the (g-1)-st symmetric power. We conjecture that the subcategory generated by our blocks has a trivial semi-orthogonal complement, proving the full BGMN conjecture. Our proof is based on an analysis of wall-crossing between moduli spaces of stable pairs, combining classical vector bundles techniques with the method of windows.